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We study the interfacial phenomenology of a fluid in contact with amicrostructured substrate within the mean-field approximation. The sculptedsubstrate is a one-dimensional array of infinitely long grooves of sinusoidalsection of periodicity length L and amplitude A. The system is modelled usingthe Landau-Ginzburg functional, with fluid-substrate couplings which correspondto either first-order or critical wetting for a flat substrate. We investigatethe effect of the roughness of the substrate in the interfacial phenomenology,paying special attention to filling and wetting phenomena, and compare theresults with the predictions of the macroscopic and interfacial Hamiltoniantheories. At bulk coexistence, for values of L much larger than the bulkcorrelation, we observe first-order filling transitions between dry andpartially filled interfacial states, which extend off-coexistence, ending at acritical point; and wetting transitions between partially filled and completelywet interfacial states with the same order as for the flat substrate (iffirst-order, wetting extends off-coexistence in a prewetting line). On theother hand, if the groove height is of order of the correlation length, onlywetting transitions between dry and complete wet states are observed. However,their characteristics depend on the order of the wetting transition for theflat substrate. So, if it is first-order, the wetting transition temperaturefor the rough substrate is reduced with respect to the wetting transitiontemperature for a flat substrate, and coincides with the Wenzel law predictionfor very shallow substrates. On the contrary, if the flat substrate wettingtransition is continuous, the roughness does not change the wettingtemperature.

Filling and wetting transitions on sinusoidal substrates: a mean-field study of the Landau-Ginzburg model